Background and Context: Computational thinking (CT) has been increasingly added to K-12 curricula, prompting teachers to grade more and more CT artifacts. This has led to a rise in automated CT assessment tools. Objective: This study examines the scope and characteristics of publications that use machine learning (ML) approaches to assess…

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Investigating properties and characteristics of unary operations is shown to be facilitated by using calculators. Several avenues for instructional exploration are suggested and examples given. These include questions relating to relations, inverses, commutativity, distributivity, and iterations. A discussion of the calculator algorithm for…

This study of seventh graders investigated the use of the calculator in learning conversion algorithms among fractions, decimals, and percents. The calculator was successful with some topics but not with others. (MP)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

The authors attempt to determine the effects of the use of direct and "combinations of tens" methods of two column-addition, ability, and grade level as factors in column addition efficiency. (MN)

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

The calculator is used to investigate properties and characteristics of certain unary operations. These include how a number is related to the number resulting from a unary operation and the result of two unary operations. A discussion of the calculator algorithm to accomplish a series of unary operations is given. Record sheets to summarize…

This experiment was conducted to determine the efficiency of three forms of an algorithm of known effectiveness and the effects of its availability following initial instruction. The dependent variable was time to solve computational problems requiring rule application. The algorithm was presented in three forms: prose, flowchart, and gradual…

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…

This report presents a theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction. The best-fitting distribution of fixation durations with a relatively simple theoretical justification…

Students from six fourth-grade classes were paired and randomly assigned to computer or worksheet treatments on multiplication and division. Those using computer-based drill-and-practice programs made greater gains on some tests of basic facts, but had no higher retention of algorithms. (MNS)

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…